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Pressure serves as a fundamental tuning parameter capable of drastically modifying all properties of matter. The advent of diamond anvil cells (DACs) has enabled a compact and tabletop platform for generating extreme pressure conditions in laboratory settings. However, the limited spatial dimensions and ultrahigh pressures within these environments present significant challenges for conventional spectroscopy techniques. In this work, we integrate optical spin defects within a thin layer of two-dimensional (2D) materials directly into the high-pressure chamber, enabling an in situ quantum sensing platform for mapping local stress and magnetic environments up to 4~GPa. Compared to nitrogen-vacancy (NV) centers embedded in diamond anvils, our 2D sensors exhibit around three times stronger response to local stress and provide nanoscale proximity to the target sample in heterogeneous devices. We showcase the versatility of our approach by imaging both stress gradients within the high-pressure chamber and a pressure-driven magnetic phase transition in a room-temperature self-intercalated van der Waals ferromagnet, Cr$_{1+\delta}$Te$_2$. Our work demonstrates an integrated quantum sensing device for high-pressure experiments, offering potential applications in probing pressure-induced phenomena such as superconductivity, magnetism, and mechanical deformation., Comment: 9 pages, 7 figures

Floquet (periodically driven) systems can give rise to unique non-equilibrium phases of matter without equilibrium analogs. The most prominent example is the realization of discrete time crystals. An intriguing question emerges: what other novel phases can manifest when the constraint of time periodicity is relaxed? In this study, we explore quantum systems subjected to a quasi-periodic drive. Leveraging a strongly interacting spin ensemble in diamond, we identify the emergence of long-lived discrete time quasi-crystals. Unlike conventional time crystals, time quasi-crystals exhibit robust sub-harmonic responses at multiple incommensurate frequencies. Furthermore, we show that the multi-frequency nature of the quasi-periodic drive allows for the formation of diverse patterns associated with different discrete time quasi-crystalline phases. Our findings demonstrate the existence of non-equilibrium phases in quasi-Floquet settings, significantly broadening the catalog of novel phenomena in driven many-body quantum systems., Comment: 7+5 pages, 4+5 figures

Periodic driving has emerged as a powerful tool to control, engineer, and characterize many-body quantum systems. However, the required pulse sequences are often complex, long, or require the ability to control the individual degrees of freedom. In this work, we study how a simple Carr-Purcell Meiboom-Gill (CPMG)-like pulse sequence can be leveraged to enhance the coherence of a large ensemble of spin qubits and serve as an important characterization tool. We implement the periodic drive on an ensemble of dense nitrogen-vacancy (NV) centers in diamond and examine the effect of pulse rotation offset as a control parameter on the dynamics. We use a single diamond sample prepared with several spots of varying NV density, which, in turn, varies the NV-NV dipolar interaction strength. Counter-intuitively, we find that rotation offsets deviating from the ideal {\pi}-pulse in the CPMG sequence (often classified as pulse errors) play a critical role in preserving coherence even at nominally zero rotation offset. The cause of the coherence preservation is an emergent effective field that scales linearly with the magnitude of the rotation offset. In addition to extending coherence, we compare the rotation offset dependence of coherence to numerical simulations to measure the disorder and dipolar contributions to the Hamiltonian to quantitatively extract the densities of the constituent spin species within the diamond., Comment: 10 pages, 6 figures

The standard quantum limit bounds the precision of measurements that can be achieved by ensembles of uncorrelated particles. Fundamentally, this limit arises from the non-commuting nature of quantum mechanics, leading to the presence of fluctuations often referred to as quantum projection noise. Quantum metrology relies on the use of non-classical states of many-body systems in order to enhance the precision of measurements beyond the standard quantum limit. To do so, one can reshape the quantum projection noise -- a strategy known as squeezing. In the context of many-body spin systems, one typically utilizes all-to-all interactions (e.g. the one-axis twisting model) between the constituents to generate the structured entanglement characteristic of spin squeezing. Motivated by recent theoretical work, here we explore the prediction that short-range interactions -- and in particular, the two-dimensional dipolar XY model -- can also enable the realization of scalable spin squeezing. Working with a dipolar Rydberg quantum simulator of up to 100 atoms, we demonstrate that quench dynamics from a polarized initial state lead to spin squeezing that improves with increasing system size up to a maximum of -3.5 dB (prior to correcting for detection errors, or approximately -5 dB after correction). Finally, we present two independent refinements: first, using a multistep spin-squeezing protocol allows us to further enhance the squeezing by approximately 1 dB, and second, leveraging Floquet engineering to realize Heisenberg interactions, we demonstrate the ability to extend the lifetime of the squeezed state by freezing its dynamics., Comment: 12 pages, 10 figures

Floquet (periodic) driving has recently emerged as a powerful technique for engineering quantum systems and realizing non-equilibrium phases of matter. A central challenge to stabilizing quantum phenomena in such systems is the need to prevent energy absorption from the driving field. Fortunately, when the frequency of the drive is significantly larger than the local energy scales of the many-body system, energy absorption is suppressed. The existence of this so-called prethermal regime depends sensitively on the range of interactions and the presence of multiple driving frequencies. Here, we report the observation of Floquet prethermalization in a strongly interacting dipolar spin ensemble in diamond, where the angular dependence of the dipolar coupling helps to mitigate the long-ranged nature of the interaction. Moreover, we extend our experimental observation to quasi-Floquet drives with multiple incommensurate frequencies. In contrast to a single-frequency drive, we find that the existence of prethermalization is extremely sensitive to the smoothness of the applied field. Our results open the door to stabilizing and characterizing non-equilibrium phenomena in quasi-periodically driven systems., Comment: 7+13 pages, 3+8 figures

Systems of spins engineered with tunable density and reduced dimensionality enable a number of advancements in quantum sensing and simulation. Defects in diamond, such as nitrogen-vacancy (NV) centers and substitutional nitrogen (P1 centers), are particularly promising solid-state platforms to explore. However, the ability to controllably create coherent, two-dimensional spin systems and characterize their properties, such as density, depth confinement, and coherence is an outstanding materials challenge. We present a refined approach to engineer dense ($\gtrsim$1 ppm$\cdot$nm), 2D nitrogen and NV layers in diamond using delta-doping during plasma-enhanced chemical vapor deposition (PECVD) epitaxial growth. We employ both traditional materials techniques, e.g. secondary ion mass spectrometry (SIMS), alongside NV spin decoherence-based measurements to characterize the density and dimensionality of the P1 and NV layers. We find P1 densities of 5-10 ppm$\cdot$nm, NV densities between 1 and 3.5 ppm$\cdot$nm tuned via electron irradiation dosage, and depth confinement of the spin layer down to 1.6 nm. We also observe high (up to 0.74) ratios of P1 to NV centers and reproducibly long NV coherence times, dominated by dipolar interactions with the engineered P1 and NV spin baths.

Optically active spin defects in van der Waals materials are promising platforms for modern quantum technologies. Here we investigate the coherent dynamics of strongly interacting ensembles of negatively charged boron-vacancy ($\mathrm{V}_{\mathrm{B}}^-$) centers in hexagonal boron nitride (hBN) with varying defect density. By employing advanced dynamical decoupling sequences to selectively isolate different dephasing sources, we observe more than 5-fold improvement in the measured coherence times across all hBN samples. Crucially, we identify that the many-body interaction within the $\mathrm{V}_{\mathrm{B}}^-$ ensemble plays a substantial role in the coherent dynamics, which is then used to directly estimate the concentration of $\mathrm{V}_{\mathrm{B}}^-$. We find that at high ion implantation dosage, only a small portion of the created boron vacancy defects are in the desired negatively charged state. Finally, we investigate the spin response of $\mathrm{V}_{\mathrm{B}}^-$ to the local charged defects induced electric field signals, and estimate its ground state transverse electric field susceptibility. Our results provide new insights on the spin and charge properties of $\mathrm{V}_{\mathrm{B}}^-$, which are important for future use of defects in hBN as quantum sensors and simulators., Comment: 8+8+4 pages, 4+5+1 figures

An outstanding challenge in large-scale quantum platforms is to simultaneously achieve strong interactions, giving rise to the most interesting behaviors, and local addressing -that can probe them. In the context of correlated phases, local addressing enables one to directly probe the nature of the system's order. Meanwhile, for out-ofequilibrium dynamics, such addressing allows the study of quantum information spreading and operator growth. Here, we introduce a novel technique that enables the measurement of local correlation functions, down to single-site resolution, despite access to only global controls. Our approach leverages the intrinsic disorder present in a solid-state spin ensemble to dephase the nonlocal components of the correlation function. Utilizing this toolset, we measure both the spin and energy transport in nuclear spin chains. By tuning the interaction Hamiltonian via Floquet engineering, we investigate the cross-over between ballistic and diffusive hydrodynamics. Interestingly, when the system is both interacting and (nearly-)integrable, we observe the coexistence of diffusive spin transport with ballistic energy transport., Comment: main text 5 pages, 4 figures; SM 10 pages 5 figures

The Kardar-Parisi-Zhang (KPZ) universality class describes the coarse-grained behavior of a wealth of classical stochastic models. Surprisingly, it was recently conjectured to also describe spin transport in the one-dimensional quantum Heisenberg model. We test this conjecture by experimentally probing transport in a cold-atom quantum simulator via the relaxation of domain walls in spin chains of up to 50 spins. We find that domain-wall relaxation is indeed governed by the KPZ dynamical exponent $z = 3/2$, and that the occurrence of KPZ scaling requires both integrability and a non-abelian SU(2) symmetry. Finally, we leverage the single-spin-sensitive detection enabled by the quantum-gas microscope to measure a novel observable based on spin-transport statistics, which yields a clear signature of the non-linearity that is a hallmark of KPZ universality., Comment: 8 pages, 5 figures + 13 pages Supplementary Information

We demonstrate that the prethermal regime of periodically driven (Floquet), classical many-body systems can host nonequilibrium phases of matter. In particular, we show that there exists an effective Hamiltonian that captures the dynamics of ensembles of classical trajectories despite the breakdown of this description at the single trajectory level. In addition, we prove that the effective Hamiltonian can host emergent symmetries protected by the discrete time-translation symmetry of the drive. The spontaneous breaking of such an emergent symmetry leads to a subharmonic response, characteristic of time crystalline order, that survives to exponentially late times in the frequency of the drive. To this end, we numerically demonstrate the existence of classical prethermal time crystals in systems with different dimensionalities and ranges of interaction. Extensions to higher order and fractional time crystals are also discussed., Comment: 8+7 pages and 3+6 figures

Conventional wisdom holds that macroscopic classical phenomena naturally emerge from microscopic quantum laws. However, despite this mantra, building direct connections between these two descriptions has remained an enduring scientific challenge. In particular, it is difficult to quantitatively predict the emergent "classical" properties of a system (e.g. diffusivity, viscosity, compressibility) from a generic microscopic quantum Hamiltonian. Here, we introduce a hybrid solid-state spin platform, where the underlying disordered, dipolar quantum Hamiltonian gives rise to the emergence of unconventional spin diffusion at nanometer length scales. In particular, the combination of positional disorder and on-site random fields leads to diffusive dynamics that are Fickian yet non-Gaussian. Finally, by tuning the underlying parameters within the spin Hamiltonian via a combination of static and driven fields, we demonstrate direct control over the emergent spin diffusion coefficient. Our work opens the door to investigating hydrodynamics in many-body quantum spin systems., Comment: 25+20+15 pages, 3+15+7 figures

The most direct approach for characterizing the quantum dynamics of a strongly-interacting system is to measure the time-evolution of its full many-body state. Despite the conceptual simplicity of this approach, it quickly becomes intractable as the system size grows. An alternate framework is to think of the many-body dynamics as generating noise, which can be measured by the decoherence of a probe qubit. Our work centers on the following question: What can the decoherence dynamics of such a probe tell us about the many-body system? In particular, we utilize optically addressable probe spins to experimentally characterize both static and dynamical properties of strongly-interacting magnetic dipoles. Our experimental platform consists of two types of spin defects in diamond: nitrogen-vacancy (NV) color centers (probe spins) and substitutional nitrogen impurities (many-body system). We demonstrate that signatures of the many-body system's dimensionality, dynamics, and disorder are naturally encoded in the functional form of the NV's decoherence profile. Leveraging these insights, we directly characterize the two-dimensional nature of a nitrogen delta-doped diamond sample. In addition, we explore two distinct facets of the many-body dynamics: First, we address a persistent debate about the microscopic nature of spin dynamics in strongly-interacting dipolar systems. Second, we demonstrate direct control over the correlation time of the many-body system. Finally, we demonstrate polarization exchange between NV and P1 centers, opening the door to quantum sensing and simulation using two-dimensional spin-polarized ensembles., Comment: 30 + 18 + 7 pages; 4 + 7 figures

Strongly disordered systems in the many-body localized (MBL) phase can exhibit ground state order in highly excited eigenstates. The interplay between localization, symmetry, and topology has led to the characterization of a broad landscape of MBL phases ranging from spin glasses and time crystals to symmetry protected topological phases. Understanding the nature of phase transitions between these different forms of eigenstate order remains an essential open question. Here, we conjecture that no direct transition between distinct MBL orders can occur; rather, a thermal phase always intervenes. Motivated by recent advances in Rydberg-atom-based quantum simulation, we propose an experimental protocol where the intervening thermal phase can be diagnosed via the dynamics of local observables., Comment: 7 + 13 pages; 4 + 15 figures

A tremendous amount of recent attention has focused on characterizing the dynamical properties of periodically driven many-body systems. Here, we use a novel numerical tool termed `density matrix truncation' (DMT) to investigate the late-time dynamics of large-scale Floquet systems. We find that DMT accurately captures two essential pieces of Floquet physics, namely, prethermalization and late-time heating to infinite temperature. Moreover, by implementing a spatially inhomogeneous drive, we demonstrate that an interplay between Floquet heating and diffusive transport is crucial to understanding the system's dynamics. Finally, we show that DMT also provides a powerful method for quantitatively capturing the emergence of hydrodynamics in static (un-driven) Hamiltonians; in particular, by simulating the dynamics of generic, large-scale quantum spin chains (up to L = 100), we are able to directly extract the energy diffusion coefficient., Comment: 6+21 pages, 4+23 figures

The idea of the out-of-time-order correlator (OTOC) has recently emerged in the study of both condensed matter systems and gravitational systems. It not only plays a key role in investigating the holographic duality between a strongly interacting quantum system and a gravitational system, but also diagnoses the chaotic behavior of many-body quantum systems and characterizes the information scrambling. Based on the OTOCs, three different concepts -- quantum chaos, holographic duality, and information scrambling -- are found to be intimately related to each other. Despite of its theoretical importance, the experimental measurement of the OTOC is quite challenging and so far there is no experimental measurement of the OTOC for local operators. Here we report the measurement of OTOCs of local operators for an Ising spin chain on a nuclear magnetic resonance quantum simulator. We observe that the OTOC behaves differently in the integrable and non-integrable cases. Based on the recent discovered relationship between OTOCs and the growth of entanglement entropy in the many-body system, we extract the entanglement entropy from the measured OTOCs, which clearly shows that the information entropy oscillates in time for integrable models and scrambles for non-intgrable models. With the measured OTOCs, we also obtain the experimental result of the butterfly velocity, which measures the speed of correlation propagation. Our experiment paves a way for experimentally studying quantum chaos, holographic duality, and information scrambling in many-body quantum systems with quantum simulators.